Question

Prove that "The lengths of tangents drawn from an external point to a Circle are equal".

Answer 1

Statement: The lengths of tangents drawn from an external point to a circle are equal.

To Prove: $PQ=PR$

Proof:

Consider a Circle with center $O$ and tangents dram from $P$ to circle at $Q$ and $R$

In $△POQ$ and $△POR$

$\angle PQO=\angle PRO$ (Right angle)

$OQ=OR$ (radii)

$OP=OP$ (common side)

So, $△POQ\simeq △POR$ (By RHS congruency)

Therefore, $PQ=PR$ (by CPCT)

Hence the statement the lengths of tangents drawn from an external point to a circle are equal is true.